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July 06, 2006

An ontological question about complex systems

Although I've been reading Nature News for several years now (as part of my daily trawl for treasure in the murky waters of science), I first came to recognize one of their regular writers Philip Ball when he wrote about my work on terrorism with Maxwell Young. His essay, now hidden behind Nature's silly subscription-only barrier, sounded an appropriately cautionary note about using statistical patterns of human behavior to predict the future, and was even titled "Don't panic, it might never happen."

The idea that there might be statistical laws that govern human behavior can be traced, as Ball does in his essay, back to the English philosopher Thomas Hobbes (1588-1679) in The Leviathan and to the French positivist philosopher Auguste Comte (1798-1857; known as the father of sociology, and who also apparently coined the term "altruism"), who were inspired by the work of physicists in mechanizing the behavior of nature to try to do the same with human societies.

It seems, however, that somewhere between then and now, much of sociology has lost interest in such laws. A good friend of mine in graduate school for sociology (who shall remain nameless to protect her from the politics of academia) says that her field is obsessed with the idea that context, or nurture, drives all significant human behavior, and that it rejects the idea that overarching patterns or laws of society might exist. These, apparently, are the domain of biology, and thus Not Sociology. I'm kind of stunned that any field that takes itself seriously would so thoroughly cling to the nearly medieval notion of the tabula rasa (1) in the face of unrelenting scientific evidence to the contrary. But, if this territory has been abandoned by sociologists (2), it has recently, and enthusiastically, been claimed by physicists (who may or may not recognize the similarity of their work to a certain idea in science fiction).

Ball's background is originally in chemistry and statistical physics, and having spent many years as an editor at Nature, he apparently now has a broad perspective on modern science. But, what makes his writing so enjoyable is the way he places scientific advances in their proper historical context, showing both where the inspiration may have come from, and how other scientists were developing similar or alternative ideas concurrently. These strengths are certainly evident in his article about the statistical regularity of terrorism, but he puts them to greater use in several books and, in particular, one on physicists' efforts to create something he calls sociophysics. As it turns out, however, this connection between physics and sociology is not a new one, and the original inspiration for statistical physics (one of the three revolutionary ideas in modern physics; the other two are quantum mechanics and relativity) is owed to social scientists.

In the mid 1800s, James Clerk Maxwell, one of the fathers of statistical physics, read Henry Thomas Buckle's lengthy History of Civilization. Buckle was a historian by trade, and a champion of the idea that society's machinations are bound by fundamental laws. Maxwell, struggling with the question of how to describe the various motions of particles in a gas, was struck by Buckle's descriptions of the statistical nature of studies of society. Such studies sought not to describe each individual and their choices exactly, but instead represent the patterns of behavior statistically, and often pointed to surprising regularities, e.g., the near-stable birth or suicide rates in a particular region. As a result, Maxwell abandoned the popular approach of describing gas particles only using Newtonian mechanics, i.e., an attempt to describe every particle's position and motion exactly, in favor for a statistical approach that focused on the distribution of velocities.

It was the profound success of these statistical descriptions that helped cement this approach as one of the most valuable tools available to physicists, and brought about some pretty profound shifts in our understanding of gasses, materials and even astrophysics. So, it seems fitting that statistical physicists are now returning to their roots by considering statistical laws of human behavior. Alas, I doubt that most such physicists appreciate this fact.

These efforts, which Ball surveys in "Critical Mass" (Farrar, Straus and Giroux, 2004) via a series of well-written case studies, have dramatically altered our understanding of phenomena as varied as traffic patterns (which have liquid, gaseous, solid and meta-stable states along with the corresponding phase transitions), voting patterns in parliamentary elections (which display nice heavy-tailed statistics), the evolution of pedestrian traffic trails across a university quad, economics and the statistics of businesses and markets, and a very shallow discussion of social networks. Although his exposition is certainly aimed at the layman, he does not shy away from technical language when appropriate. Pleasantly, he even reproduces figures from the original papers when it serves his explanations. Given that these phenomena were drawn from a burgeoning field of interdisciplinary research, it's easy to forgive him for omitting some of my favorite topics, treating others only shallowly, and mercifully leaving out the hobby horses of cellular automata, genetic algorithms and artificial life.

Now, after seeing that list of topics, you might think that "Critical Mass" was a book about complex systems, and you might be right. But, you might be wrong, too, which is the problem when there's no strict definition of a term. So, let's assume he has, and see what this offers in terms of clarifying the corresponding ontological question. For one thing, Ball's choices suggest that perhaps we do not need other ill-defined properties like emergence, self-organization or robustness (3) to define a complex system. Instead, perhaps when we say we are studying a "complex system," we simply mean that it has a highly heterogeneous composition that we seek to explain using statistical mechanisms. To me, the former means that I, because of my limited mental capacity to grasp complicated equations, relationships or a tremendously large configuration space, pretty much have to use a statistical characterization that omits most of the detailed structure of the system; also, I say heterogeneous because homogeneous systems are much easier to explain using traditional statistical mechanics. The latter means that I'm not merely interested in describing the system, which can certainly be done using traditional statistics, but rather in explaining the rules and laws that govern the formation, persistence and evolution of that structure. For me, this definition is attractive both for its operational and utilitarian aspects, but also because it doesn't require me to wave my hands, use obfuscating jargon or otherwise change the subject.

In general, it's the desire to establish laws that reflects complex systems' roots in physics, and it is this that distinguishes it from traditional statistics and machine learning. In those areas, the focus seems to me to be more on predictive power ("Huzzah! My error rate is lower than yours.") and less on mechanisms. My machine learning friends tell me that people are getting more interested in the "interpretability" of their models, but I'm not sure this is the same thing as building models that reflect the true mechanical nature of the underlying system... of course, one fundamental difference between much of statistical learning and what I've described above is that for many systems, there's no underlying mechanism! We shouldn't expect problems like keeping the spam out of my inbox to exhibit nice mechanistic behavior, and there are a tremendous number of such problems out there today. Fortunately, I'm happy to leave those to people who care more about error rates than mechanisms, and I hope they're happy to leave studying the (complex) natural world, mechanisms and all, to me.

Updates, July 7

(1) The notion of the tabula rasa is not antithetical to the idea that there are patterns in social behavior, but patterns per se are not the same as the kind of societal laws that the founders of sociology were apparently interested in, i.e., sociology apparently believes these patterns to be wholly the results of culture and not driven by things that every human shares like our evolutionary history as a species. I suppose there's a middle ground here, in which society has created the appearance of laws, which the sociophysicists then discover and mistake for absolutes. Actually, I'm sure that much of what physicists have done recently can be placed into this category.

(2) It may be the case that it is merely the portion of sociology that my friend is most familiar with that expresses this odd conviction, and that there are subfields that retain the idea that true mechanistic laws do operate in social systems. For all I know, social network analysis people may be of this sort; it would be nice to have an insider's perspective on this.

(3) Like the notions of criticality and universality, these terms actually do have precise, technical definitions in their proper contexts, but they've recently been co-opted in imprecisely ways and are now, unfortunately and in my opinion, basically meaningless in most of the complex systems literature.

posted July 6, 2006 07:09 PM in Reviews | permalink